I wish I knew the type of interface to use. I am not an expert in microwave components, but I'm researching as time permits. Also, at 2.4503 GHz, it's going to be pretty large. Did you calculate the wave velocity for that mode?

Todd

Todd:

Apologies for the late response, school has been taking quite a lot of time...

The group velocity for a box width of 7.07 cm would be 1.5 E8 m/s. Unfortunately I am not very experienced with antennas either and don't know how to store energy in the cavity while simultaneously injecting it into the frustum. I'll keep researching and discuss with a few professors to gain some more insight.

May I suggest using a curved mirror as it results in greater relational movement of the laser dot. You may find them in some hardware shops? or some womens makeup departments according to my daughter.

At a minimum you will need two strings, one for front, one for rear of the unit. This will minimise sideways /rotational translation which would mask effects. Keep each string separate and attach each to the roof.

If you still get sideways torque/momentum due to induced mechanical events derived from the switching on/off of the magnetron etc then you may require 4 strings, one on each "corner" of the unit.

Arc:

A curved mirror sounds like a good solution. I will have to do some calculations to determine what curvature is appropriate.

As for balancing the pendulum, two strings will probably be sufficient. I imagine hanging the frame will be a challenge, but luckily we will have plenty of time to figure out the little details once we start constructing. We will start construction mid June and will be experimenting until September. We have no other obligations and I have heard no one else needs the vacuum chamber over the summer.

Does anyone have any recommendations for the thickness of sheet metal to buy? Clearly we want something structurally sound that won't warp very much when heated, but we also want minimal mass on the pendulum. I think 1/16 inch will be a good balance. I am planning to buy enough metal to make a copper and aluminum frustum and hopefully have enough copper leftover to try the separate symmetric cavity connected to the aluminum frustum. I'll also buy some PTFE and maybe HDPE as well.

There are several people that think the same way (that it cries out for a space test), while there are several other ones that think it would be premature. Since you made a powerful argument for the energy paradox, it would be useful if you could list all the reasons (and what and how should be tested) why a space test should be the next step, as a powerful argument in that direction may help to push the ball rolling...upwards

I am happy that you found my position on the energy paradox powerful. But speaking of premature, some further mulling and reading - ongoing - tells me that there may well be a third possibility for the behaviour of the thrust over time. If this "third thrust scenario" turns out to be the correct one, then the EmDrive may not be useful for any kind of propulsion, and would at best remain as an interesting test framework for various physics variants.

A third thrust scenarioAgain we assume that the measured thrust is actual. We note its two characteristics:a) It is measured as a static force.b) It remains constant as long as input power is applied to this static configuration.'a)' implies that we can only theorise as to its dynamic behaviour - i.e. when the EmDrive moves over time.

I take together two further pieces of information:1. Shawyer's video of the moving EmDrive2. Mike McCulloch's MiHsC theory of operation.Now of course, there are a variety of interpretations possible for both of these. For example, that the video is flawed because all the angular momentum is being supplied by imperfections in the air bearing. Or that Mike's theory is nonsense because it violates GR. And so forth. So here I have to decide what to assume so as to justify this 3rd scenario. So here I choose:1. The vid shows that an impulse is produced which results in a real and constant momentum of the EmDrive.2. The theory predicts the same thing - constant forward EmDrive momentum.

And so this third thrust scenario is this:As soon as the EmDrive is free to move, a definite and constant momentum is established and its thrust falls to zero.

So far, so good. But given this third thrust scenario is the correct one, what then is expected to happen when we switch off the power?

Have you tried this one yet?

P = F*v = m*a*v

P/a = m*v = constant

m*a = - v*dm/dt

Lose mass at the same rate at which the remaining mass gains velocity, then the ratio of acceleration to power will remain constant, while there is mass remaining to lose. Total Energy can never go over unity because by definition, the momentum is constant and it's losing mass. Any paradox here?

COMSOL's website says the RF module can do far field calculations, and the antenna placement would appear to put at least part of the frustum in the near field. It looks by eyeball that the software is only looking at the far field being reflecting off the small end of the frustum.

Or am I missing something?

This COMSOL Finite Element Analysis solution is a numerical solution of Maxwell's differential equations, taking into account the boundary conditions, including the losses responsible for the finite Q. What you are looking at is the steady state of the electromagnetic fields.

The steady state electromagnetic field solution are standing waves. Although the initial condition is not symmetrical, due to travelling waves, this is a very-short-lived transient, as the solution soon reaches a (practically) symmetric steady state.

This has been shown by @aero with a very interesting movie based on a 2D solution of the truncated cone as a flat trapezium using MEEP which is a Finite Difference code (free from MIT alumni) that performs the full transient solution. It was neat to see how the (practically) symmetric steady state was soon reached starting from an unsymmetric initial condition.

Furthermore, as pointed out by RotoSequence, the steady state solution for the magnetic field and a COMSOL thermal analysis was corroborated by temperature measurements using an infrared thermal camera, which verifies that the heating is due to induction heating from the magnetic field.

I obtained an exact solution for the symmetric steady state (which of course does not take into account the initial unsymmetric transient) and it fully verifies NASA's COMSOL FEA steady state solution for the electromagnetic field: the natural frequency is within 1% of the exact solution and the mode shapes are extremely close (I posted the exact solution comparison some time ago).

If one is interested in near-field far-field, transient, fully complex solution (including initial travelling waves morphing into standing waves, as well as evanescent waves) then one has to resort to a time-marching solution as with MEEP finite difference approach or a [FEA in space/FD in time] solution that imposes a finite element discretization in space and a finite difference time discretization. (Such a transient, 3D solution containing evanescent waves is extremely time consuming.)

Highlighted above in red. This very short lived transient is the key to everything. The aspect of this that we need to find ways to exploit further.

And while on the subject of simulation: Guido Fetta of Cannae tells me that his COMSOL(?unsure) sim predicts a nonzero net Lorentz force for his device. Now, we all learned that no closed system of currents can produce such a net force. There's a paradox. He insists that there are no significant cumulative rounding errors.

Anyone have insight into this?

There cannot be a paradox.

Let's remember that the COMSOL FEA solution is the steady state solution showing the spatial distribution of the field. Remember that the steady state solution of Maxwell's differential equations can be accomplished by separation of variables.

The harmonic (time varying) part of the field is assumed. So, for example, the Magnetic Field shown on the COMSOL output is the spatial distribution of the magnetic field. Now, what is shown as a maximum and what is shown as a minimum is arbitrary, since depending at what time one arbitrarily chooses to display the magnetic field, as the magnetic field varies with time like a harmonic function.

Similarly, the Poynting vector is a harmonic function of time, and this is, as you point out, well known in the literature, with a frequency which is twice the frequency of the magnetic and the electric field.

Although the spatial distribution of the Poynting vector is non-zero at arbitrary points in time, over a whole cycle the Poynting vector (and the Lorentz force) for a cavity sums up to exactly zero, just like the mean of the magnetic and electric fields is also zero. COMSOL is an excellent package.

The Poynting vector solution of Maxwell's equations points towards the Big Base half of the time, and points towards the Small Base half of the time.

COMSOL will not tell that to the analyst obtaining a steady solution where the harmonic function of time is implicit. It is recommended that COMSOL and any other FEA packages (ANSYS MultiPhysics, etc., ABAQUS, ADINA, NASTRAN) should be run by experienced FEA analysts, to prevent errors. (Ditto for FD, control volume , and any other numerical packages).

@deltaMass, you're on the right track. We've shown that the utility of COMSOL in figuring out this problem is limited as COMSOL is considering the standing wave and isn't considering the traveling wave. It gives no consideration to what is happening over extended time (over multiple full cycles) or to what is happening to a resonant cavity under dynamic operation, for example while under acceleration. COMSOL provides no insight as to what is happening when the resonant cavity is being excited by FM or other sources of phase noise. Building off the comments about COMSOL's ability to simulate mode shapes..that was proven to be accurate by Paul March's thermal shots here:

It is my understanding, from what Paul March wrote, that the main controlling parameter in determining the thrust generation performance of the EM-Drive is the rate of phase modulation of the RF signal that is injected into the resonant cavity.

This requires an FM modulated signal of around 100 kHz deviation that dithers back and forth around the resonant cavity's resonant frequency as fast as possible.

That main controlling parameter should not be taken lightly.

See Mr. Shawyer's comments in the screenshot about how the standing wave is constructed by addition of a traveling wave which is IN PHASE with the standing wave. Those of us who regularly work with electronics know about constructive and destructive interference, and this mechanism applied here is what puts energy into and takes energy out of the standing wave within the cavity.

If I present a signal at the loop probe (or dipole or waveguide slot) which is in phase with the standing wave, energy will couple into the cavity. If I present a signal at the loop probe (or dipole or waveguide slot) which is out of phase with the standing wave, energy will couple out of the cavity. This works both ways. The way Paul March mentioned, and what Shawyer mentions as motor/generator mode.

We can create the effects by the above method that mimic what a photon would experience in an accelerating box. This box is a quantum harmonic oscillator which can only resonate at precise discrete frequencies. This all reminds me of @Notsosureofit's AFR thrust equation.

Sure, but I wouldn't use a wrench in place of a screwdriver either. The utility of COMSOL should not be extended past where it is useful. COMSOL has no usefulness beyond the "knowns." The unknowns can't be simulated. See Paul March & Mr. Shawyer's comments in this post, in screenshots and quotes.

Let's not forget that Mr. Shawyer (the inventor of EMdrive) is telling us to NOT get hung up on the standing wave, see screenshot:

The standing waves inside the frustum are simply a large potential energy store. Those standing waves still have to be put to use to get work out of them. From what Shawyer and Paul March have told us, there are two known ways......So far we've uncovered two ways; 1) Introducing phase noise into the excitation signal *, 2) Accelerating the cavity **. Both of these play off the same theme, which is that a resonant cavity will only resonate at a narrow frequency range within its bandwidth. If energy within that cavity is shifted out of that narrow bandwidth, it will no longer resonate, thus an energy deficit to be filled by the traveling wave.

*Theorized before, now proven by Paul March:http://forum.nasaspaceflight.com/index.php?topic=36313.msg1366823#msg1366823http://forum.nasaspaceflight.com/index.php?topic=36313.msg1331792#msg1331792**Red shift/Blue shift changes the phase. Also see Shawyer's comments here: http://www.emdrive.com/EmDriveForceMeasurement.pdf and here: see motor/generator mode comments http://www.emdrive.com/IAC13paper17254.v2.pdf***Possible 3 is I've been toying around with the idea of using phase shift keying as a means to modulate the excitation signal, this approach is similar to what Paul March was talking about using FM, but using PSK keeps the signal on resonant frequency peak, while varying the phase. So this keeps the frequency the same, but flips the phase, so it might not work. I know from experience that a PSK signal as viewed on a spectrum analyzer is a distribution above and below CF. I envision varying the symbol rate as a means to control thrust. I believe the directionality from both Paul's and my PSK idea comes from two sources, 1) The helicity of the polymer chains, 2) non-reciprocity within the cavity, which I've posted papers on. For now I acknowledge there is no proof of any non-reciprocity or PT symmetry breaking (either alone or as a pair) happening within Emdrive, yet I expect it will be coming.****Possible 4, excite EMdrive with two signals on separate cables. I know these cavities can support multiple modes at ones, so why not exploit that, see where it goes?https://goo.gl/nosWnF

I have succeeded in making a safe stable balance (finally), but I am still absolutely bombing in my attempts to get power to the balance. The slip ring approach has its faults and I'm going to have to find some sort of flexible power pickup or abandon the whole slip ring idea altogether. If I stick with this approach, I'll never get anywhere near the sensitivity of Cavendish.

If I go to flying a battery and use DC-DC converters (http://www.amazon.com/dp/B00JUFJ1GA?psc=1) to power the electronics, any future of high power testing using this setup will be dashed. Not to mention I'll have to go to a much stronger torsion wire or a Dyneema braid (as opposed to the solid Dyneema line I'm using now) to hold everything up. As I know, engineering is a bunch of tradeoffs.

I have succeeded in making a safe stable balance (finally), but I am still absolutely bombing in my attempts to get power to the balance. The slip ring approach has its faults and I'm going to have to find some sort of flexible power pickup or abandon the whole slip ring idea altogether. If I stick with this approach, I'll never get anywhere near the sensitivity of Cavendish.

If I go to flying a battery and use DC-DC converters (http://www.amazon.com/dp/B00JUFJ1GA?psc=1) to power the electronics, any future of high power testing using this setup will be dashed. As I know, engineering is a bunch of tradeoffs.

I have succeeded in making a safe stable balance (finally), but I am still absolutely bombing in my attempts to get power to the balance. The slip ring approach has its faults and I'm going to have to find some sort of flexible power pickup or abandon the whole slip ring idea altogether. If I stick with this approach, I'll never get anywhere near the sensitivity of Cavendish.

If I go to flying a battery and use DC-DC converters (http://www.amazon.com/dp/B00JUFJ1GA?psc=1) to power the electronics, any future of high power testing using this setup will be dashed. Not to mention I'll have to go to a much stronger torsion wire or a Dyneema braid (as opposed to the solid Dyneema line I'm using now) to hold everything up. As I know, engineering is a bunch of tradeoffs.

Great news, hopefully all those replication attempts by individuals or small teams will shed light on relevant parameters, and you are on the forefront. Can't you you go battery without DC/DC, what are the DC requirement of your RF amplifier ?

Yes, the mass equivalent of the energy delta. That is very very small, has potential chemical energy mass even ever been weighted experimentally ? Also this very very small mass would, eventually, just been transferred as heat in the cavity's walls. A hot brick is heavier than a cold brick, by the same amount a battery loses mass to heat it. Ultimately this mass_energy is radiated away as IR, either isotropically (0 net momentum) or collimated (net momentum no better than photon rocket). Just saying, from conventional interpretations of conventional frameworks.

Following on what jknuble said about the multipactor-like effect as a possible cause of thrust. http://en.wikipedia.org/wiki/Multipactor_effect I can't help but wonder about what's going on with the copper surface of the frustum. A quick back of the envelope (well, python) calculation shows that there's certainly enough energy in these devices to somehow atomize a small amount of copper , and propel them with enough momentum to produce a small amount of thrust.

For example, a 30 watt emdrive where 0.001% of the energy went towards atomization and 1% went toward addtional momentum of the particles... You'd have a device with 91uN thrust, propelling 1.4ng of copper a second at 65500m/s.

I can think of 3 ways to debunk this. 1) perhaps that amount of particles going that fast would be noticeable with the naked eye, so this isn't really a valid explanation. 2) stick a detector behind the thruster (are they ionized?). 3) SEM of the surface compared to scraps from the same batch of copper not used in the thrustum.

Just how would we get a net-thrust from a closed cavity with atomization. Even if atoms are being ioniozed inside the cavity I don't see how that could result in a net thrust. Atomization results in immediate thrust but then that creates impact on the other side of the cavity canceling out the propulsion.

For the last month I've been digging through the mountains of well thought out (some not so well thought out) material, tests and ideas of why this EM Drive does what it does. It's a beautiful conundrum. For over 40 years as an engineer I've built/designed/tested computers, electronics, electro-mechanical, semiconductor machines, imaging systems for the Super Conductor Super Collider , the list is long. Not a single thing I built defied the laws of physics or the formulas of the trade. . . Maxwell, Ohms law, etc. If something didn't work for some weird reason, it still followed the basic laws and formulas when it ended up.It doesn't really matter to me what is happening inside of the EM Chamber it must follow the principals of physics and conservation of energy and momentum is one of them. If I have a Air Tank pressurized with 200psi of air and a audio speaker inside that can blast at 100 watts any frequency range no matter what mixture of sound or what mixture of harmonics I crank, the tank will not move, but put a hole in one end and stand back. The second law of thermodynamics states that the entropy of an isolated system never decreases and the EM Chamber is an isolated enclosed system, we think. If we are getting thrust that, thrust must be acting outside the chamber in some form. This is why I asked the simple question if smoke was used in the tests, it wasn't to detect thermal air currents but to see if it was moving away from any thrust from the EM Chamber. Smoke is small .5 to 2 um and might be be directly effected. If not then look for other forms of accelerated energy, providing thrust emanating out of the EM Chamber. Frobicat said "Appears the only compulsory casualty is apparent CoE, not necessarily CoE in itself if one can find a suitable positive energy source (or a negative energy sink) and a mechanism to couple with such source (or sink to get rid of debt).How the (few) other theories out there deal with the apparent CoE demise" ?

Just my 2 cents on this Rocky Mountain Snowy Morning. FWIW A hot tub in the snow is a great place to simply think. Michelle

I've never heard of that before. If you had a fully charged capacitor that was wired in series with a switch and resistor where would the mass be lost when the switch was closed? Note: The paper quoted above does not provide any proof of the claim. The "Mach Guitar" experiment was inconclusive.

I have succeeded in making a safe stable balance (finally), but I am still absolutely bombing in my attempts to get power to the balance. The slip ring approach has its faults and I'm going to have to find some sort of flexible power pickup or abandon the whole slip ring idea altogether. If I stick with this approach, I'll never get anywhere near the sensitivity of Cavendish.

If I go to flying a battery and use DC-DC converters (http://www.amazon.com/dp/B00JUFJ1GA?psc=1) to power the electronics, any future of high power testing using this setup will be dashed. Not to mention I'll have to go to a much stronger torsion wire or a Dyneema braid (as opposed to the solid Dyneema line I'm using now) to hold everything up. As I know, engineering is a bunch of tradeoffs.

There must be some way of coupling the RF power to the cavity using feed horns or near-field antennas. That would eliminate the need to weigh down the balance with a PA, batteries or achive a workable cummutator. There may not be much gain at the frequency of interest but all you want to do is to transmit a fraction of the power. Maybe 2 identical collinear dipoles would work. The recieve dipole, mounted on the outside of the cavity, would connect to the internal loop used to drive the cavity. If you have access to a network analyzer you could optimize the match and maximize the return loss.

There must be some way of coupling the RF power to the cavity using feed horns or near-field antennas. That would eliminate the need to weigh down the balance with a PA, batteries or achive a workable cummutator. There may not be much gain at the frequency of interest but all you want to do is to transmit a fraction of the power. Maybe 2 identical collinear dipoles would work. The recieve dipole, mounted on the outside of the cavity, would connect to the internal loop used to drive the cavity. If you have access to a network analyzer you could optimize the match and maximize the return loss.

Beaming RF power directly is tempting for the reasons you say, but wouldn't that introduce a momentum coupling between the fixed dipole and the one on the balance ? Even assuming a cylindrical wave guide coaxial with rotation axis, the E and B fields would have a definite transverse favorite direction (there are experts here, please correct me if wrong), the fields from fixed parts and geometry of the cavity would not be symmetrical under rotation of the cavity, no rotation invariance => potential energy variation with rotation => torque. Can that be (classically) quantitatively estimated ? Maybe it's much lower torque coupling than energy transfer alternatives (thin wire or rotating wet contacts for DC to RF amp.) so still interesting option...

This could allow for a very light freely rotating setup (consider magnetic bearings instead of just point contact on jewel cup, or just a floater on a cup full of liquid, goal is lowest stiction as possible, not necessarily ultra-low dynamic viscosity as net thrust can always be integrated as cumulative displacement) :

Not a single thing I built defied the laws of physics or the formulas of the trade. . . Maxwell, Ohms law, etc. If something didn't work for some weird reason, it still followed the basic laws and formulas when it ended up.It doesn't really matter to me what is happening inside of the EM Chamber it must follow the principals of physics and conservation of energy and momentum is one of them. If I have a Air Tank pressurized with 200psi of air and a audio speaker inside that can blast at 100 watts any frequency range no matter what mixture of sound or what mixture of harmonics I crank, the tank will not move, but put a hole in one end and stand back. The second law of thermodynamics states that the entropy of an isolated system never decreases and the EM Chamber is an isolated enclosed system, we think. If we are getting thrust that, thrust must be acting outside the chamber in some form. This is why I asked the simple question if smoke was used in the tests, it wasn't to detect thermal air currents but to see if it was moving away from any thrust from the EM Chamber. Smoke is small .5 to 2 um and might be be directly effected. If not then look for other forms of accelerated energy, providing thrust emanating out of the EM Chamber.

I too would like to see a smoke test. I can't see conservation of momentum being violated. It just goes against everything we know both empirically and theoretically. I think that even in the off chance that the EmDrive is not experimental error, conservation of momentum will still hold albeit in a more subtle manner than the classical analysis would expect.

You gave the illustrative example of a closed container with different traveling and standing waves of different frequencies and amplitudes bouncing around inside. There is a very neat quantum mechanical reason that such a container is not truly closed. Even in an infinite potential well, the wave function can extend outside the walls of the well, leading to effects such as tunneling. Another great example of the wavefunction extending beyond barriers that appears to be somewhat related to the possible effect seen here is the Aharanov Bohm effect: http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect. This is due to the wavefunction of a particle outside of a container extending past the barrier of the container and interacting with the EM field on the inside of the container.

Now I leave this paper to ruminate upon:http://arxiv.org/abs/0708.0681Perhaps the EmDrive is acting as an evanescent mode photon rocket where momentum is carried away outside the cavity via this mechanism.

EDIT: Please click on the above link to see the above quotation which is not reproduced in full in order to save bandwidth

A) We should make an effort to properly characterize Finite Element solution packages like COMSOL that are able to obtain solutions to a large number of physical problems. COMSOL is not just a "wrench" but a whole tool box of solutions.

the utility of COMSOL in figuring out this problem is limited as COMSOL is considering the standing wave and isn't considering the traveling wave. It gives no consideration to what is happening over extended time (over multiple full cycles) or to what is happening to a resonant cavity under dynamic operation, for example while under acceleration. COMSOL provides no insight as to what is happening when the resonant cavity is being excited by FM or other sources of phase noise.

In this case, "COMSOL" is being used as shorthand for "an eigenvalue solution to Maxwell's equations in a cavity." The fact that the COMSOL numerical solution provides an accurate solution for the natural frequencies and mode shapes of a cavity is not questionable.

1) To calculate the natural frequencies of the truncated cone cavity, so that they know at what frequency they can excite resonance at a high Q.

2) To calculate the Q for the different mode shapes.

3) To calculate the different mode shapes (whether they are transverse magnetic or transverse electric modes) and the field distributions for different modes.

4) To calculate the resulting temperature from induction heating by the magnetic field (those calculations compare very well with the temperatures measured by a thermal camera).

NASA Eagleworks did not use the COMSOL Finite Element analysis to calculate any thrust forces.

Of course, it is well known by the NASA Eagleworks team that any claimed interaction with the Quantum Vacuum does not have any appreciable effect on the above calculated quantities (which are solely based on Maxwell's equations). NASA Eagleworks has not reported any force calculations (based on Maxwell's stress tensor) or Poynting vector calculations based on Maxwell's equations. They have stated that they are aware that such force calculations would give zero net thrust.

Dr. White's calculations for the thrust are based on a separate code, which reportedly he wrote based on his Quantum Vacuum conjecture. I have not seen the actual formulation for this code, or anything addressing what his code is based on, so I will not comment any further on his attempt.

Returning to COMSOL's capabilities, of course it is well known that one can also conduct a transient solution to the problem using COMSOL. It is well known that a transient solution to Maxwell's equations cannot result in a solution that will explain the claims of the EM Drive being able to be used for space propulsion.

NASA conducted an eigenvalue problem solution of Maxwell's equations, in order to obtain the natural frequencies and mode shapes for the cavity. This makes eminent sense. Concerning FM modulation, COMSOL can also be used to obtain a solution (if so desired) for an arbitrary spectrum as an input (and the variation of the spectrum vs. time). None of this is going to change the natural frequencies of the cavity, nor is it going to explain (just based on Maxwell's equations) how an EM Drive can be used for space propulsion.

No solution, eigensolution or transient solution, solely based on Maxwell's equations, can explain a violation of conservation of momentum, as the equations being solved by COMSOL (in this particular analysis: Maxwell's equations) fully satisfy conservation of momentum.

the standing wave is constructed by the addition, in phase, of a continuous travelling wave. This travelling wave results in the forces that are produced on the end plates which are orthogonal to the group velocity vector of the wave. In a cavity with the correct radius spherical end plates there is no force on the side walls due to the travelling wave, because the walls are parallel to the group velocity vector

This claim that there are no forces on the side walls is contradicted by a calculation of Maxwell's stress tensor, particularly under classical mechanics, as explicitly shown by Greg Egan (http://gregegan.customer.netspace.net.au/SCIENCE/Cavity/Cavity.html ) for example for such a truncated cone with spherical ends. Shawyer (to my knowledge) has never adequately answered Greg Egans's proof.

C) I am also surprised by Shawyer invoking Cullen

Quote from: Shawyer

The forces produced by travelling waves in a waveguide were first investigated theoretically and experimentally by Prof. Alex Cullen back in the 1950s. His analysis is as true today as it was when he first did the work

Never mind that Cullen was not the first to investigate theoretically the forces produced by travelling waves in a waveguide (as Cullen himself points out that he is using the much older intuitive derivation by Sir J.J.Thompson, which is well-known to be fully consistent with the derivation due to Maxwell himself). Cullen was the first, in 1950, to experimentally measure quantitatively the radiation pressure at microwave frequencies (for light frequencies, it had been done back in 1900 by Lebedew, as it is well known).

The analysis and experiments performed by Cullen were based on waveguides with constant cross-section. In such waveguides Maxwell's stress tensor components on the side walls are self-cancelling due to the fact that the waveguide has constant cross-section. This is completely inapplicable to a truncated cone or any such geometry where the cross-section is not constant. For a geometry with variable cross-section Maxwell's stress tensor components are not self-cancelling (as follows trivially from vector analysis) and hence must be taken into account when calculating the net thrust under classical mechanics and special relativity, which unfortunately Shawyer has failed to do.

SUMMARY: COMSOL Finite Element Analysis can accurately solve a huge range of classical, nonlinear, anisotropic, coupled, transient, and physical problems based on classical mechanics. All COMSOL solutions satisfy the universal laws of conservation of momentum and conservation of energy.

The issue of conservation of momentum and energy in the EM Drive has not yet been formally and satisfactorily addressed. Valiant attempts are being conducted in this forum to explain the EM Drive thrust (if it is not an artifact) on the basis of General Relativity or other physical solutions that lie outside the range of classical mechanics addressed by COMSOL.

Understandably at this early stage of analysis, these attempts at solutions remain to be formally proven and remain to be shown to quantitatively predict EM Drive measurements (even within engineering accuracy, and much less to scientific accuracy).

I was thinking about superposition and whether mass and energy are conserved when two waves cancel. If that were not the case then perhaps there could be an imbalance in the frustrum that causes there to be an asymmetric photon pressure buildup on each face of the frustrum. I found this article in my travels that seems to suggest this but it is behind a paywall (doubtless I would not understand it anyway):

We added the two elliptically polarized waves and computed the energy–momentum density of their sum. We showed that energy and momentum are not generally conserved, except when the two waves are moving in opposite directions. We also showed that the momentum of the superposition has an extra component perpendicular to the propagation directions of both waves. But when we took the time-average of the energy and momentum of the superposition, we found that the time-average energy and momentum could also be conserved if both waves are circularly polarized but with opposite handedness, regardless of the directions of the two waves. The non-conservation of energy and momentum of the superposition of two elliptically polarized plane waves is not due to the form of the plane waves themselves, but rather to the accepted definitions of the electromagnetic energy and momentum. Perhaps we may need to modify these definitions in order to preserve the energy–momentum conservation. In our computations, we restricted ourselves to the superposition of two waves with the same frequency.

.. There is a very neat quantum mechanical reason that such a container is not truly closed. Even in an infinite potential well, the wave function can extend outside the walls of the well, leading to effects such as tunneling. Another great example of the wavefunction extending beyond barriers that appears to be somewhat related to the possible effect seen here is the Aharanov Bohm effect: http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect. This is due to the wavefunction of a particle outside of a container extending past the barrier of the container and interacting with the EM field on the inside of the container....

A warm welcome to the forum and thank you for a great post.

I think we all agree with you regarding the above statement.

One of the people in this forum (@aero) has pursued such an explanation with numerical calculations using MEEP (a freely available computer code using the Finite Difference numerical discretization approach). Unfortunately, due to computer memory and computer time available, @aero's calculations have been restricted to a 2-D formulation modeling the 3D truncated cone as a flat 2-D trapezium (which obviously cannot appropriately model the 3D problem).

The problem is that the EM Drive researchers claim thrust/InputPower measurements that are thousands of times greater than the one of a perfectly collimated photon rocket.

It would be most interesting to this forum if you could lead us to an explanation that could explain how the EM Drive can result in thrust/InputPower measurements that are thousands of times greater than the one of a perfectly collimated photon rocket.

You gave the illustrative example of a closed container with different traveling and standing waves of different frequencies and amplitudes bouncing around inside. There is a very neat quantum mechanical reason that such a container is not truly closed. Even in an infinite potential well, the wave function can extend outside the walls of the well, leading to effects such as tunneling. Another great example of the wavefunction extending beyond barriers that appears to be somewhat related to the possible effect seen here is the Aharanov Bohm effect: http://en.wikipedia.org/wiki/Aharonov%E2%80%93Bohm_effect. This is due to the wavefunction of a particle outside of a container extending past the barrier of the container and interacting with the EM field on the inside of the container.

Now I leave this paper to ruminate upon:http://arxiv.org/abs/0708.0681Perhaps the EmDrive is acting as an evanescent mode photon rocket where momentum is carried away outside the cavity via this mechanism.[/quote]

Thank you, more hot tub thinking.Nice paper on tunneling and it does make sense on how the waves with quantum mechanical tunneling cross the plane of incidence (Goos-Hänchen shift). (Back in school studying Tunneling diodes we couldn't understand how they worked). Should I say that a tunnel (quantum or not) is a hole in the air tank or EM Device? What comprises the pressure and how do we detect it, that's the big question isn't it?

As far as I understand, everything in physics is a process. That logically includes all kinds of conservation mechanisms.

Question is: Are processes like CoM and CoE finite or infinite? If we can't even tell whether or not these processes are finite or not, this whole discussion is perhaps all moot. If these processes are finite, I think it would mean that all apparent momentum and energy return to the QV anyways.I think it's become clear for everyone that within Maxwell's linear framework no thrust whatsoever is possible from within such a closed cavity. Key will be the experimental data of Eagleworks around summertime to show whether or not expected improved 'thrust' signatures can be obtained in a methodical and controlled manner.What also might happen is that some random day Mr. Shawyer's device makes it to the public in form of a powerful in-your-face demonstrator that leaves all people dumb-struck. Same for the 'Cannae' device. For now, I think it's best to wait for results from Eagleworks this summer. They have had the best visibility so far.